#include <Eigen/Eigenvalues>
#include <iostream>
using namespace Eigen;
using namespace std;
void main() {
	MatrixXd X = MatrixXd::Random(5,5);
	MatrixXd A = X + X.transpose();
	cout << "Here is a random symmetric 5x5 matrix, A:" << endl << A << endl << endl;
	SelfAdjointEigenSolver<MatrixXd> es;
	es.compute(A);
	cout << "The eigenvalues of A are:" << endl << es.eigenvalues() << endl;
	cout << "The matrix of eigenvectors, V, is:" << endl << es.eigenvectors() << endl << endl;
	double lambda = es.eigenvalues()[0];
	cout << "Consider the first eigenvalue, lambda = " << lambda << endl;
	VectorXd v = es.eigenvectors().col(0);
	cout << "If v is the corresponding eigenvector, then lambda * v = " << endl << lambda * v << endl;
	cout << "... and A * v = " << endl << A * v << endl << endl;
	MatrixXd D = es.eigenvalues().asDiagonal();
	MatrixXd V = es.eigenvectors();
	cout << "Finally, V * D * V^(-1) = " << endl << V * D * V.inverse() << endl;
	return;
}
